Intel® oneAPI Math Kernel Library (oneMKL) - Data Parallel C++ Developer Reference
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trsm_batch
Computes a group of trsm operations.
Description
The trsm_batch routines are batched versions of trsm, performing multiple trsm operations in a single call. Each trsm solves an equation of the form op(A) * X = alpha * B or X * op(A) = alpha * B.
trsm_batch supports the following precisions:
T |
|---|
float |
double |
std::complex<float> |
std::complex<double> |
trsm_batch (Buffer Version)
Buffer version of trsm_batch supports only strided API.
Strided API
Strided API operation is defined as:
for i = 0 … batch_size – 1
A and B are matrices at offset i * stridea and i * strideb in a and b.
if (left_right == side::left) then
compute X such that op(A) * X = alpha * B
else
compute X such that X * op(A) = alpha * B
B = X
end for
where:
op(A) is one of op(A) = A, or op(A) = AT, or op(A) = AH
alpha is a scalar
A is either m x m or n x n triangular matrix
B and X are m x n general matrices
On return, matrix B is overwritten by solution matrix X.
For strided API, a and b buffers contains all the input matrices. The stride between matrices is given by the stride parameters. Total number of matrices in a and b buffers is given by batch_size parameter.
Syntax
namespace oneapi::mkl::blas::column_major {
void trsm_batch(sycl::queue &queue,
oneapi::mkl::side left_right,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t m,
std::int64_t n,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
std::int64_t stridea,
sycl::buffer<T,1> &b,
std::int64_t ldb,
std::int64_t strideb,
std::int64_t batch_size,
compute_mode mode = compute_mode::unset)
}
namespace oneapi::mkl::blas::row_major {
void trsm_batch(sycl::queue &queue,
oneapi::mkl::side left_right,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t m,
std::int64_t n,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
std::int64_t stridea,
sycl::buffer<T,1> &b,
std::int64_t ldb,
std::int64_t strideb,
std::int64_t batch_size,
compute_mode mode = compute_mode::unset)
}
Input Parameters
- queue
-
The queue where the routine should be executed.
- left_right
-
Specifies whether matrices A are on the left side or right side of the multiplication. See Data Types for more details.
- upper_lower
-
Specifies whether matrices A are upper or lower triangular. See Data Types for more details.
- trans
-
Specifies op(A), transposition operation applied to matrices A. See Data Types for more details.
- unit_diag
-
Specifies whether matrices A are unit triangular or not. See Data Types for more details.
- m
-
Number of rows of matrices B. Must be at least zero.
- n
-
Number of columns of matrices B. Must be at least zero.
- alpha
-
Scaling factor for the solution.
- a
-
Buffer holding input matricees A. Size of the buffer must be at least stridea * batch_size.
- lda
-
Leading dimension of matrices A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.
- stridea
-
Stride between two consecutive A matrices.
- b
-
Buffer holding input/output matrices B. Size of the buffer must be at least strideb * batch_size.
- ldb
-
Leading dimension of matrices B. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.
- strideb
-
Stride between two consecutive B matrices.
- batch_size
-
Specifies number of triangular linear systems to solve.
- mode
-
Optional. Compute mode settings. See Compute Modes for more details.
Output Parameters
- b
-
Output buffer overwritten by batch_size solution matrices X.
trsm_batch (USM Version)
USM version of trsm_batch supports group API and strided API.
Group API
Group API operation is defined as:
idx = 0
for i = 0 … group_count – 1
for j = 0 … group_size – 1
A and B are matrices in a[idx] and b[idx]
if (left_right == side::left) then
compute X such that op(A) * X = alpha[i] * B
else
compute X such that X * op(A) = alpha[i] * B
end if
B = X
idx = idx + 1
end for
end for
where:
op(A) is one of op(A) = A, or op(A) = AT, or op(A) = AH
alpha is a scalar
A is either m x m or n x n triangular matrix
B and X are m x n general matrices
On return, matrix B is overwritten by solution matrix X.
For group API, a and b arrays contain the pointers for all the input matrices. The total number of matrices in a and b are given by:
Syntax
namespace oneapi::mkl::blas::column_major {
sycl::event trsm_batch(sycl::queue &queue,
const oneapi::mkl::side *left_right,
const oneapi::mkl::uplo *upper_lower,
const oneapi::mkl::transpose *trans,
const oneapi::mkl::diag *unit_diag,
const std::int64_t *m,
const std::int64_t *n,
const T *alpha,
const T **a,
const std::int64_t *lda,
T **b,
const std::int64_t *ldb,
std::int64_t group_count,
const std::int64_t *group_size,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
namespace oneapi::mkl::blas::row_major {
sycl::event trsm_batch(sycl::queue &queue,
const oneapi::mkl::side *left_right,
const oneapi::mkl::uplo *upper_lower,
const oneapi::mkl::transpose *trans,
const oneapi::mkl::diag *unit_diag,
const std::int64_t *m,
const std::int64_t *n,
const T *alpha,
const T **a,
const std::int64_t *lda,
T **b,
const std::int64_t *ldb,
std::int64_t group_count,
const std::int64_t *group_size,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
Input Parameters
- queue
-
The queue where the routine should be executed.
- left_right
-
Array of group_countoneapi::mkl::side values. left_right[i] specifies whether matrices A are on the left side or right side of the multiplication in group i. See Data Types for more details.
- upper_lower
-
Array of group_countoneapi::mkl::uplo values. upper_lower[i] specifies whether matrices A are upper or lower triangular in group i. See Data Types for more details.
- trans
-
Array of group_countoneapi::mkl::transpose values. trans[i] specifies op(A), transposition operation applied to matrices A in each group i. See Data Types for more details.
- unit_diag
-
Array of group_countoneapi::mkl::diag values. unit_diag[i] specifies whether matrices A are unit triangular or not. See Data Types for more details.
- m
-
Array of group_count integers. m[i] specifies number of rows of matrices B in group i. All entries must be at least zero.
- n
-
Array of group_count integers. n[i] specifies number of columns of matrices B in group i. All entries must be at least zero.
- alpha
-
Array of group_count scalar elements. alpha[i] specifies scaling factors for the solutions in group i.
- a
-
Array of total_batch_count pointers for input matrices A. See Matrix Storage for more details.
- lda
-
Array of group_count integers. lda[i] specifies leading dimension of matrices A in group i. Must be at least m[i] if left_right[i] = side::left or at least n[i] if left_right[i] = side::right. All entries must be positive.
- b
-
Array of total_batch_count pointers for input/output matrices B. See Matrix Storage for more details.
- ldb
-
Array of group_count integers. ldb[i] specifies leading dimension of matrices B in group i. Must be at least m[i] if column major layout or at least n[i] if row major layout is used. All entries must be positive.
- group_count
-
Number of groups. Must be at least zero.
- group_size
-
Array of group_count integers. group_size[i] specifies the number of trsm operations in group i. Each element in group_size must be at least zero.
- mode
-
Optional. Compute mode settings. See Compute Modes for more details.
- dependencies
-
Optional. List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.
mode and dependencies may be omitted independently; it is not necessary to specify mode in order to provide dependencies.
Output Parameters
- b
-
Array of pointers to output matrices B overwritten by total_batch_count solution matrices X.
Return Values
Output event to wait on to ensure computation is complete.
Strided API
Strided API operation is defined as:
for i = 0 … batch_size – 1
A and B are matrices at offset i * stridea and i * strideb in a and b.
if (left_right == side::left) then
compute X such that op(A) * X = alpha * B
else
compute X such that X * op(A) = alpha * B
B = X
end for
where:
op(A) is one of op(A) = A, or op(A) = AT, or op(A) = AH
alpha is a scalar
A is either m x m or n x n triangular matrix
B and X are m x n general matrices
On return, matrix B is overwritten by solution matrix X.
For strided API, a and b arrays contain all the input matrices. The stride between matrices is given by the stride parameters. Total number of matrices in a and b arrays is given by batch_size parameter.
Syntax
namespace oneapi::mkl::blas::column_major {
sycl::event trsm_batch(sycl::queue &queue,
oneapi::mkl::side left_right,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t m,
std::int64_t n,
T alpha,
const T *a,
std::int64_t lda,
std::int64_t stridea,
T *b,
std::int64_t ldb,
std::int64_t strideb,
std::int64_t batch_size,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
namespace oneapi::mkl::blas::row_major {
sycl::event trsm_batch(sycl::queue &queue,
oneapi::mkl::side left_right,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t m,
std::int64_t n,
T alpha,
const T *a,
std::int64_t lda,
std::int64_t stridea,
T *b,
std::int64_t ldb,
std::int64_t strideb,
std::int64_t batch_size,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
Input Parameters
- queue
-
The queue where the routine should be executed.
- left_right
-
Specifies whether matrices A are on the left side or right side of the multiplication. See Data Types for more details.
- upper_lower
-
Specifies whether matrices A are upper or lower triangular. See Data Types for more details.
- trans
-
Specifies op(A), transposition operation applied to matrices A. See Data Types for more details.
- unit_diag
-
Specifies whether matrices A are unit triangular or not. See Data Types for more details.
- m
-
Number of rows of matrices B. Must be at least zero.
- n
-
Number of columns of matrices B. Must be at least zero.
- alpha
-
Scaling factor for the solution.
- a
-
Pointer to input matricees A. Size of the array must be at least stridea * batch_size.
- lda
-
Leading dimension of matrices A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.
- stridea
-
Stride between two consecutive A matrices.
- b
-
Pointer to input/output matrices B. Size of the array must be at least strideb * batch_size.
- ldb
-
Leading dimension of matrices B. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.
- strideb
-
Stride between two consecutive B matrices.
- batch_size
-
Specifies number of triangular linear systems to solve.
- mode
-
Optional. Compute mode settings. See Compute Modes for more details.
- dependencies
-
Optional. List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.
mode and dependencies may be omitted independently; it is not necessary to specify mode in order to provide dependencies.
Output Parameters
- b
-
Pointer to output matrix B overwritten by batch_size solution matrices X.
Return Values
Output event to wait on to ensure computation is complete.